Electrostatic precipitators such asthese remove 96 percent of the dustfrom converter gases.

A summary of water recycling inCanadian mills by Pickett and Joe'.shows that recycling in gravity andmagnetic concentration circuits aswell as simple flotation circuits canand is being used in the majority ofcases. Serious problems arise inPb-Zn and Pb-Zn-Cu selective flo-tation circuits. The second seriousproblem area is the cyanide gold in-dustry. Recycling is limited bybuild-up of complex chemical com-pounds which affect metallurgy andsulfates that cause ot:erating prob-lems. Uranium leaching plants havedeveloped expensive but effectiverecycling systems. The most effec-tive overall answer is a cascade pondsystem. Often the reclaimed waterfrom thickeners, filters, and tailingpond can be matched with require-ments for each part of the circuitwith the most effective combinationof the chemical properties of theprocess, the ore, and the reagents.

Tailings and Reclamation

International experts reported" ontailing dam construction and opera-tion, water reclamation, and vege-tation of tailings at the InternationalTailings Symposium in Tucson, Ari-zona. Representatives from twenty-two countries heard 35 technical pa-pers and inspected two tailingsdams. Many of the papers includedstabilization techniques. The papersare published in a Tailings Sympo-sium book "Tailing Disposal 'l'oday."

References, O'Brian, B., "Envlronmental Quality

Roundup;' Mining Congress Journal, VoL 59,No.7, 11/73, pp. 811-89,

. C1M .'orum, CJM Bulleti.., VoL 66, No,

734, 1973, p. 11.I "Emphasizing Environment," Mining E..-

gineering, VoL ~, No.1, 1973, p. 19.. "Washington Impact," E&MJ, VoL 174,

No. 10, 1973, p. 13.. Dasher, J., "Hydrometallurgy for Cop~

Concentrates?" CIM Bulletin, VoL 88, No. 733,1973, p. 48.

. "Federal Water Pollution Control Act,What Mining Industry Must Do To Comply,"World Mining, Vol 9, No.3, pp. 44-49.

., "Deadlines and Judicial Review Under theWater Pollution Act;' Mining Congreu JOUT-nal, VoL 59, No. I, 1973, p. 81,

a O'Brian, B., "The New Water PollutionControl Act;' Mining Congreu Journal, Vol59, No.3, 1973, PP. 38-45.

a O'Brian, B., "Environmental QualityRoundup," Mining Congreu Journal, Vol 59,No.4. 1973. P. 98.

.. "F/otation Cell Removes Metals from Mill

Effluent," World Mining. Vol 8, No. 13, 1973,p.17.

11 Sharp. F. H. and Clifford, K. L., "Re-cycling Milling Water In Missouri's New 1.eadBelt," Mining Engineering, Vol. 25, No.7,1973, pp. 88-72-

,. Bullock, R. L., "Mine-Plant DeaiCD PhlI-osophy Evolves from St. Joe's New Lead BeltOperations," Mining Congra8 JouTnal, Vol59. No.5, 1973, P. 20-29.

,. Pickett, D. E. and Joe, E. G., "Water Re-cycling ExpensIve In Canadian Mills," paperpresented at the 1973 AIME annual meetingin Chicago. submitted for publication.

,. "Tailing Disposal Today: Bigger SaferDams for Higher Tonnages." World Mining,Vol 8, No. 13, 1912, p. 26-31.

13 "Humphrey Resoils and Replants MinedOut Ti Sands," World Mining, Vol 9, No. a.1973, P. 41,

MINING ENGINEERS MINING ENGINEERING 77

FundamentalsP. Somasundaran

Henry Krumb School of MinesColumbia University

J.HerbstDepartment of Mining.Metallurgical and Fuels

EngineeringThe University of Utah

R. SmithMackay School of Mines

University of Nevada

Treatment of fines for recoveringvaluables in them and for processingthem into a disposable form has re-ceived increased attention duringthe past year. Particles in the sub-micron range are hard to separate.JIowever. increased fine-grinding by

'-industry makes it necessary to findmethods for processing such parti-cles without causing major environ-mental problems. At the 10th Inter-national Mineral Processing confer-ence,' Clark examined the possibleuse of various techniques such asflotation, differential precipitation,liquid/liquid separation, and mag-netic separation for treatment offines. Selective ftocculation, plannedfor processing hematite ore from theTilden mine in the Michigan upperpeninsula, was discussed by Readand Whitehead at the same meeting.An interesting suggestion there wasthat of Visman and Hamza and in-volves the use of flocculants duringthe treatment of fines with classifiercyclones. New processes have beendescribed recently for enhanced de-watering of phosphate slime, Theseinclude considerable enhancement ofslime sedimentation by appropriateadditions of particles coarser thanthe slime itself; sand is sufficient forthe purpose,' Clarity of the recov-ered water, which is important forrecycling, remained excellent. An-other technique that appears prom-ising for dewatering of slime utilizesseepage of water through porousmaterials dispersed within theslurry," Regarding flotation, it hasbeen proposed that the mechanismwhereby gangue slimes reduce se-lectivity is slime carryover into thewater layer attached to the air bub-ble, the thickness of which increasesif excess frother is used,'

Mechanism of sulfide minerals fto-tat ion has continued as a major re-search topic, the nature of the spe-cies responsible for flotation usingxanthates still being the main ques-tion, Allison, et aI," reported that thesurface reaction product of xan-thates on sulfide minerals will beeither metal xanthates or dixantho-gens depending on the type of nUn-eral and its electrode potentials. Anearlier discussion by Allison, et aI.

has been critically examined in arecent review by Guttierrez" on themechanism of xanthate flotation ofgalena. At the annual AWE meet-ing in Chicago, Wells and VanCleave presented a hypothesis thatthe hydrophobicity of galena in xan-thate solution is due to adsorptionand reduction of diethyl dixantho-gen on other parts followed by ditJu-sion of dixanthogen to cathodicareas. However, Nicol' has claimedthat diethyl dixanthogen is not aproduct at the galena surface. Varia-tion in rest potentials was attributedto chan,es in the nature of the ga-lena electrode used. Adsorptionproperties of xanthate species onsulfide minerals have been corre-lated by Prasad" and by Kuhn andM. C. Fuerstenau (annual AIMEmeeting). The higher stability of di-xanthogen on galena than on mostother sulfides has been correlated byPrasad with the matching of inter-atomic distances of galena's minerallattice to that of the dixanthogenmolecule. A study of Eh response ofsulfide minerals as a function of pHby Natarajan and Iwasaki" shows themeasured Eh to approach that ofnoble metals under certain condi-tions. This phenomenon is possiblydue to the formation of a passivelayer on sulfides which in turn couldbe responsible for a decrease in re-sponse of these sulfides to flotationor leaching. Other noteworthy worksusing sulfides includes that of vanLierde1O on the depression effect oflow molecular weight polyacrylatesin xanthate flotation of galena andthat of BanerjiU on the activation ofsphalerite using copper ions gener-ated from an electrode instead offrom CuSO.. The role of sulfide ionsin the flotation of malachite aftersulfidization is, according to Satoand Laskowski, IS to reduce flotation.Elimination of sulfide either byaeration in the presence of malachiteor by the decantation of supernatantliquid enhances flotation.

Chemistry of fiotation and fioccu-lation was discussed at a specialsymposium on this topic at the 47thNational Colloid symposium.'" Dis-cussions at this symposium startedwith a plenary lecture by M. C.Fuerstenau on the mechanism ofsurfactant adsorption on oxides andsilicates. For copper oxide-carboxyl-ate systems Coelho and Poling pre-sented spectroscopic evidence for thepresence of carboxylate anions as amajor component in the first ad-sorbed layer on copper oxides andcopper carboxylates and organicacid species as the major compo-nents in subsequent layers. Aplan,et aI, demonstrated the significanceof point defects, at least in the caseproduced by Cd'. in AgCI, on theflotation of AgCl, using amine ascollector. The use of hydrocarbongases in flotation was discussed bySomasundaran and Moudgil. Satura-tion of the collector solution withhydrocarbon gases was found to

In the laboratory. a cnemist prepares liquid samples for atomic absorption(spectrophotometer) and related testing.

78 FEBRUARY 1974 SOCIETY OF

cause a significant increase in sul-fonate flotation of alumina but notin that of hematite, which floats withsulfonate, or in that of quartz, whichdoes not float. Thus, the possible useof hydrocarbon gases for improvingselectivity in flotation is suggested.

some light on the actual nature ofspecies interactions that are largelydependent on the number of -CH~groups in the surfactant. Influenceof the number of -CH~ groupsin the alkyl chains of sulfonate onwettability of alumina in aqueoussolutions has been quantitativelystudied by Wakamatsu and D. W.Fuerstenau" using contact anglemeasurements. An additional systemfor which van der Waals associationhas been found to be the major fac-tor determining adsorption is that ofzircon-oleate aqueous solution.'. Theeffect of a number of CF ~ groups inflotation was examined by Somas-undaran and Kulkarni." Perftuoro-carboxylic acids were found to besuperior collectors compared to cor-responding carboxylic acids. partic-ularly for flotation in acid pulps.

A number of studies"""""'" havebeen made on flotation systems con-taining fluorides. Kitchener and co-workers have examined the impor-tant role of reactions at the solid-solution interface on adsorption offluoride by alumina, feldspar, andquartz. HF activation of cationic flo-tation of feldspar was attributed toan increase in the negative zeta po-tential of the mineral. Continuedstudies on the properties of apatiteby Somasundaran and Agar-"' haveyielded information of the role ofphosphate, calcium and fluoride ions.

Role of gas bubbles and adsorp-tion on them has received recent at-tention. Using dynamic surface ten-sion measurements, Fincb andSmith~ have studied the time de-pendence of mine adsorption at theair/liquid interface as a function ofpH and discussed the influence ofthis kinetics on the ability of a bub-ble to act as transferring agent ofcollector to the mineral surface.Other studies on this aspect includethat of Viswanathan and Majum-dar~ on the migration of collectortowards the bubble-mineral contactperimeter and that by Dibbs, et al,"'on the role of surface charge on gasbubbles on flotation.

tinued in 1973. Research concernedwith the scale-up design of the largemills~ suggests that grinding effi-ciency increases with increasing milldiameter to about 12.5 feet afterwhich increased size no longer yieldsincreased efficiency. Energy size-re-duction relationships remained atopic of research.

Agar and Somasundaran at theTenth International Mineral Proc-essing congress demonstrated theequivalence of several existing re-lationships; Austin:: has discussedambiguities associated with thechoice of a "characteristic particlesize" for use in the general grinding"law" proposed by Walker in 1937;while RumpF has proposed a newrelationship based on an analysis ofcomminution from a fracture physicsviewpoint. Jomoto and Majima havepresented an empirical relationshipbetween tensile strength. criticaldrop height and ball mill grindabil-ity."~ In the area of size distributionrepresentation, Harris*' has pre-sented further arguments concern-ing the use and interpretation ofWeibull distribution plots.

Mathematical Modeling

Interest in the development ofmathematical models for mineralprocessing systems has been high forthe last ten years. During this period

researchers frequently mentioned, if

only in passing, that the ultimate

objectives of modeling studies in-clude improvement in the design,

optimization and control of mineralprocessing unit operations. This year

several investigators have begun ex-

ploring in some detail various indus-

trial applications for these models.

Research concerned with the appli-

cation of physically based, popula-

tion balance models, to tumblingmill scale-up design by Herbst, et al,

presented at the Tenth International

Mineral Processing congress, bySnow, presented at the International

Conference and Instrument Exhibi-tion in Particle Technology in Chi-cago," by Austin~ and Faruja, et al-

has shown rather clearly the short-

comings of traditional design

schemes (e.g. Bond's approach) andsuggests that a scheme based on the

more detailed models will yield sig-nificant improvements in the ac-

curacy of design. Other work with

these models as described at the

Eleventh International Symposiumon Computer Applications in the

Minerals Industry'" by Root and

White and by Horst, et aI, suggests

that they may provide an idealframework for identifying new

grinding circuit control strategiesand testing them off-line by simu-lation. Flotation research in South

Africa (NIM)~ has resulted in what

appears to be a practical phenome-nological model for use in the de-

sign and control of complex flotationcircuits. Similar applications ori-ented flotation modeling has been

Scope and limitations of thermo-dynamic methods involving deter-mination of such parameters as heatof adsorption have been examinedby Mellgren, et aI, at the 10th In-ternational Mineral Processing con-ference. At the same meeting Predaliand Cases presented a detailed ther-modynamic interpretation of sur-factant adsorption and van derWaals association on homogeneousand heterogeneous surfaces. Ther-modynamics of van der Waals asso-cia~ion between chains at solid-liq-uid interfaces has been studied"measuring adsorption of dodecylsulfonate on alumina as a functionof temperature and computingchanges in heat and entropy of ad-sorption at herni-micelle concentra-tion. Results obtained have thrown

Comminution

One of the most controversial re-search items in comminution in 1973was the Snyder process, a possiblealternative to conventional size re-duction in which particle fracture isinduced by the sudden release of air,gas or steam under pressure.!-; Thedevelopers have made several claimsfor the process, e.g. higher metal-lurgical efficiency due to better lib-eration and lower capital and oper-ating costs; verification of theseclaims awaits carefully documentedplant scale testing.

Continuing research and develop-ment on grinding circuit controlschemes and on-line size analyzersis resulting in an increasing numberof installations of commercial con-trol systems. Trend.~ in the accept-ance of large diameter mills con-

MINING ENGINEERS MINING ENGINEERING 79

"Effect of Alkyl SuUonates on the WettabU-Ity of Alumina..' Trans. SMEI AIM£, ZS4(.June 1973), p. 123.

... Dixit, S. G. and Biswas. A. K., "Studieson Zircon-Sodium Oleate Flotation System:I-Solid-Liquid Interfacial Parameters..' Trans.IMM. BZ (802). (September 1973), p. CI40.

17 Somasundaran, P. and Kulkarni, R. D.,"Effects of Chain LenCth of Perftuorosurfac-tants as Collectors," Trans. lMM, 81. (8021(September 1973), p. CI64.

'0 Iskra, J., Guttierre~, C. and Kitchener,.J. A., "Influence of Quebracho on the Flota-tlon of Fluorite. Calcite, Hematite. andQuart~ with Oleate as Collector," Trans. IMM,81. (7991. (1973). p. C73.

'8 Shergold. H. L.. "Infrared Adsorption ofSOdium DodecylsuUate by Calcium Fluoride."Trans. IMM, 81 (3) (September 1973), p.C148.

-Warren, L. .1. and Kitchener,.1. A.. "Roleof Fluoride In the Fl!'tation of Feldspar: Ad-sorption on Quartz. Corundum and PotassiumFeldspar," Trans. IMM, 81 (31 (September1972), P. C137,

A Somuundaran, P. and Apr, G, Eo, "Fur-ther Streaming Potential Studies on ApatiteIn Inorganic Electrolytes." Trans, SMEI AIME.1.51. (31 (September 19721, p. 348.

"Finch..J. A. and Smith, G. W., "DynamicSurface Tension of Alkaline DodecylamlneAcetate Solutions In Oxide Flotation," Trans.IMM, 81 (793) (December 19721, p. C213.

,. Vlswanathan. It. V. and Majumdar,K. K., "The Mechanism of Collector andRegular Interaction In the Flotation of BeachSand Mlnerals." .J. Mines Metals Fuels. ZO(1972). p. 106... Dlbbs, H. P., Sirois. L, L. and Bredln, R.,"The Role of Gas Bubbles in the Flotationof Quartz," Res. Rep. MInes Branch Can. R248, (1972).:D Cavanauch. W, J., "Snyder ProeeD-ABreakthrou8h In ComminuUon, H M1nJn1 Con-cress .Journal, Dec. 1972, p. 30.. Rowland, C. A., .Jr., "Comparlson ofWork indices Calculated from Operatinc datawith those from Laboratory Test Data," XIMPC, London, Paper 38, April 1973.

Sf Austin, L. G., "A Commentary on theKick., Bond and Rlttlnaer Laws of Grindlnc,"Powdcr Technology, 7, 1973, p. 315.. Rumpf, H., "Physlcal Aspects of Com-minution and New Foundation of a Law ofComminution," Powder Technology, 7. 197a.p.l45.. .Jomoto, It. and Majlma. H., "Criterion ofComminution," C1M Transactions, VoL 'IS,Dec. 1972. p. 68.

*' Harris, C. C., "The Alyavdln-WeibuU Plotof Grlndlnc Data and the Order of Kinetics,"Powder Technolocy. 7, 1973. p. 123.

81 international Conference and InstrumentExhibition In ParUcie Technology, Chicago,AulUSt 1973.

.. AusU, L. G., "UnderBtandin& Ball MIllSWnI." Indo Chem. Process DeL DeveloPH11., No.2, 1973, p. 121.

.. FargJa, M., Nakajima, Y. and Tanaka, T.,"Design of Closed-Circult GrtndlnC Systemwith Tube Mm and Nonldeal ClassIfier," Ind.Chern. Process Des. Develop., 11., No.1, 1973,p. 18.

.. Eleventh International Symposium onComputer Applications in the MlneraJa In-dustry, Untv. of Arizona, April 1973-

-Kin&. R. P., Puih, G. and Lan'ley. .JH"ApplicaUon of a Flotation Model to an In-dustrial Plant." HIM Report No. 1562, Uni-versity of Natal, .July 1973.

-Kina. R. P., "An Analytical Solution tothe Batch-Comminution EquaUon," .Tournaiof the South African Institute of MInInC andMetallurgy, Nov. 1972, p. 127,

87 Nakajtma, Y. and Tanaka, T., "Solutionof Batch Grinding EquaUon, " Ind. Eng.Clem. Process Des. Develop., 11., No. I, 1973.p.25.

.. Herbst. .J. A. and Kim, .T. H., "Nearl,Equal Selection Functions In Linear Size Dis-cretized Grindina Models." Trans. 1MM. 'Z,1973. p. C189.. Olsen, T. O. and Krogh, S. R., "Mathe-matical Model of Grlndinc at Dltrerent Con-ditIons In Ball Mill..' Trans. SAIEI AIME. 252(1972), p. 452.

~ Kelsall, D. F., Stewart, P. S. B. and Wei-ler, It. R., "Continuous Grindlnl In a SmallWet Ball Mill, Part IV. A Study of the In-ftuence of Grindlnc Medta Load and Den-slty," Powder Technology, 7. 1973, p. 293.

.. Reyes. G. W.. Itelsall, D. r. and Stewart.P. S. B., "Contlnuous Grindina In a SmallWet Rod Mill. Parts I, n," Powder Technol-ogy, 7,1973. P. 319... Austin, L. G. and ShojL K., .. An Ex-planation of Abnormal Breakage of LarleParticle Size In Laborator7 MUla," PowderTechnology. 7, 1973, p. 3.

.. Hogg. R. and Fuentenau, D. W.. "PowerRelationships for Tumblinl Mills." Trans.SMEI AIME, 1.51., December 19'/2, p. 418.

.. ShoJI. K., Hogg. R. and Austin, L. G.,., Axtal Mixing of Particles In Batch BallMm.," Powder Technology, 7. 1973, p. 331.

"Sastry, K. V. S. and Fuerstenau, D. W.."Memanism of AgIlomerate Growth in GreenPelleUzatlon." Powder TechnoloiY. 7, 1973,p.97.

Fitch at the International Confer-ence and Instrument Exhibition inParticle Technology and a methodfor identifying classifier parametersfrom experimental data describedby Luckie and Austin at the TenthInternational Mineral Processingcongress. Efforts in agglomerationhave resulted in the identification offive distinct mechanisms of forma-tion and growth in wet pelletization(nucleation, coalescence, abrasiontransfer, breakage and snowbal-ling.'"

Pxocess improvement appears tobe a viable means to economic gainin mineral processing operations inthe U.S. during the next decade.Since a quantitative understandingof existing processes is essential todevelopment of effective improve-ment schemes, research concernedwith the fundamentals of MineralProcessing unit operations must beintensified. The required programscan only be carried out with thesupport and active participation ofU.S. industry in this area. Coopera-tive research efforts of this type be-tween industry, academia and gov-ernment agencies in several othercountries e.g. Australia, South Af-rica, Canada, Japan and Finland, ap-pear to be yielding significant re-turns in their respective mineral in-dustries.

References, 10th International mineral processin. con-

ference, LDndon, April 1873.. Somaeundaran, p" Smith. E. L., Jr" andBarril, C. C., "Effect of Coarser Particles onthe Settlin. Cbaracteriltics of PhosphaticSlimes," 1st International Particle Technol-ocy Conference Proceedings, I.I.T., C1icaCO(August 1873), p. 1M.

. MoudeU, B. M., Onoda, G. Y.. Jr., andWhitney, E. D., "The Seepaae Tecbnlque forthe Dewaterinl of Phosphate sUmes," to bepresented at the l03rd AlirE annual meetin&Dallas, February 1874-

. Waksmundski, Neczaj-Hruzewicz. J., andPlanch, M., "Mechanism of Carryover ofGanf:Ue Slimes durin. FlotaUon of SulfurOre,' Trans. IMM. 8J (783) (December 1872).p. C248.. Allison. S. A., et aJ, "A Determination ofthe Products of Reaction Between VariousSulfide Minerail and Aqueous Xanthate So-iution and a Correlation of the Products withElectrode Rest ~tentia1a," Metan. Trans.,N.Y., 3 (October 1872), p. 2613.

. Guttierrez, C.. "The Mechanism of Flota-tion of Galena by Xanthates," Miner. Sci.Engra., .s (2) (April 18731. p. 108.

f Nicol, M. J.. «A Preliminary Electrochem-ical Investiaation of the Galena-Xanthate-Oxycen System in Aqueous SoluUon," Nato.lost. Metall., Ref. No. 1447, July 1872.. Prasad. M. S., «Mechanism in SulfideFlotation by the Collector Action of DIxan-toolen.." Trans. Indian Institute of Metals.(February 1873) p. 42.

. Natarajan. K. A. and Iwasaki, I., «Eh-pHresponse of Noble Metal and Sulfide MineralElectrodes," Trans. SME/AIME. 1$1 (4)(1872). p. 437.

,. Van LIerde, A., «Effects of Acrylate Poly-mers on the Sulphldization Flotation of Cop-per, Lead. and Zinc Oxide Ores auoda~with a Carbonate Gancue," Trans. IMM, 8J(783) (1872), p. C204.

U Banerji, B. K.. «A new Technique for theActivation of Sphalerite," Pro«:. Australas.lnst. Min. Metall. no. 245, March 1873, p. 33.

u Soto, H. and Laskowski, J.. "Redox Con-ditions in the Flotation of Malachite with aSulphidizin. alent," Trans. lMM, 82 (8021(September 1873), p. C157.

u FlotaUon and Alliomeration: Theory andPracUce, 47th National Colloid s7mposiumlonc abstracts. Ottawa. June 18-20, 1873.

'4 Somasundaran, P. and Fueratenau, D. W.."H~at and Entropy of Adsorption and A88O-dation of Lon. Chain Surfactant. at the Alu-mina-Aqueous Solution Interf~,'. Tr8J18.SME/AlME.2$1 (3) (September 1872). p. 2'15-

II Wakamatsu, T. and J'uerstenau. D, W..

described by Steiner at the TenthInternational Mineral Processingcongress and by Johnson and Lynchat the Eleventh International Sym-posium on Computer Applications inthe Mineral Industry.

In addition to research concernedwith the direct use of models forprocess improvement considerableeffort has been devoted to the re-finement of existing models and thedevelopment of new ones for a vari-ety of unit operations. Two pa-perS-': have dealt with special solu-tions of the integrodifferential ~ua--f.hft AI hath ~in.. Sfudies, re--po--i~bt"Gardner at the AIMEAnnual Meeting in Chicago, involv-ing linear size discretized populationbalance models have produced ana-lytical solutions for the dynamics ofball mill start-up and the responseto a step change in feed size dis-tribution. Further, it has been con-firmed computationally that the un-equal selection function assumptionfrequently invoked in the solution ofthese model equations does not placeany practical limitations on theirusefulness." The influence of ballmill operating variables (mill speed,ball loaq, ball siZe, etc.) on theparameters of population balancemodels has been examined byHerbst and D. W. Fuerstenau (pre-sented at the AIME Annual Meetingin Chicago), by Olsen and Krogh-and by Kelsall, et al" with a viewtoward extending the simulation ca-pabilities of these models. Otherstudies have been concerned withmodel comparison and verification incontinuous mills; lumped and dis-tributed transport population bal-ance models as well as matrix mod-els have been examined in thesestudies. A recent computationalstudy by Mika and presented at theInternational Conference and In-strument Exhibition in ParticleTechnology has led to the rathersurprising conclusion that in spiteof the fact that the population bal-ance models are fundamentally moresound, matrix models can be madeto provide an equally good descrip-tion of steady state grinding circuitbehavior. Additional experimentalevidence has been presented for theexistence of nonlinear breakage be-havior in certain tumbling mill sys-tems"'" and a paper concerned withthe use of linear approximations tononlinear kinetic behavior was pre-sented by Herbst and Mika at theEleventh International Symposiumon Computer Applications in theMinerals Industry. Two other me-chanical aspects of tumbling millbehavior (power draft and particlemixing) which must be accuratelymodeled in order to develop a com-pletely predictive milling descrip-tion were also treated in recentstudies."'"

Other modeling research reportedin 1973 includes the development ofa unified model for classification ofparticles in fluids reported on by

SOCIETY OF80 FEBRUARY 1974